3 papers
math.AC2026
Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov +1
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart po…
math.GR2024
Monotone parameters on Cayley graphs of finitely generated groups
Martin Kassabov, Igor Pak
We construct a new large family of finitely generated groups with continuum many values of the following monotone parameters: spectral radius, critical percolation, and asymptotic…
math.CO2024
All triangulations have a common stellar subdivision
Karim Adiprasito, Igor Pak
We address two longstanding open problems, one originating in PL topology, another in birational geometry. First, we prove the weighted version of Oda's \emph{strong factorization…